Design: Blocked Cluster RCT, with 3 levels, and randomization done at level 2 (school level).

Models: random and fixed treatment effects.

Default parameters:

  • M = 3
  • J = 30
  • K = 10
  • rho: \(\rho\) = 0.5
  • ATE ES = 0.125, 0.125, 0.125
  • R21, R22: \(R^2_1\) = 0.1, 0.1, 0.1, \(R^2_2\) = 0.1, 0.1, 0.1
  • ICC2: \(\text{ICC}_2\) = 0.2, 0.2, 0.2
  • Omega: \(\omega_2\) = 0, \(\omega_3\) = 0.1

Parameters by model type:

  • R23: \(R^2_3 = 0\) for fixed effects model, \(R^2_3\) = 0.1, 0.1, 0.1 for random effects model
  • ICC3: \(\text{ICC}_3 = 0\) for fixed model, \(\text{ICC}_3\) = 0.2, 0.2, 0.2 for random effects model

Power Validation

Base case

Varying school size

\(\bar{n}\) = 100

\(\bar{n}\) = 75

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6

\(R^2_3 =\) 0.6, 0.6, 0.6

\(R^2_1 =\) 0, 0, 0 \(R^2_2 =\) 0, 0, 0 \(R^2_3 =\) 0, 0, 0

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.125, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.7, 0.7, 0.7

\(\text{ICC}_3\) = 0.7, 0.7, 0.7

\(\text{ICC}_2\) = 0, 0, 0

## NULL
## NULL

\(\text{ICC}_2\) = 0.2, 0.2, 0.2

Varying Omega

\(\omega_3\) = 0.8

\(\omega_3\) = 0 \(\text{ICC}_3\) = 0.2, 0.2, 0.2

\(\omega_3\) = 0.8 \(\text{ICC}_3\) = 0.7, 0.7, 0.7

Kappa

\(\kappa\) = 0.4

## NULL

MDES validation

## 
## 
## +------------+---------------+---------------+-------------+
## |    MTP     | Adjusted MDES | D1indiv Power | Target MDES |
## +============+===============+===============+=============+
## |    rawp    |     0.077     |     0.138     |    0.125    |
## +------------+---------------+---------------+-------------+
## | Bonferroni |     0.125     |     0.138     |    0.125    |
## +------------+---------------+---------------+-------------+
## |     BH     |     0.125     |     0.222     |    0.125    |
## +------------+---------------+---------------+-------------+
## |    Holm    |     0.123     |     0.167     |    0.125    |
## +------------+---------------+---------------+-------------+
## 
## Table: d3.2_m3rr2rc

Sample size validation

## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |      J      |     30      |     0.221     |
## +------+-------------+-------------+---------------+
## | Holm |      J      |     30      |     0.172     |
## +------+-------------+-------------+---------------+
## 
## Table: d3.2_m3rr2rc
## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |      K      |     11      |     0.223     |
## +------+-------------+-------------+---------------+
## | Holm |      K      |     10      |     0.171     |
## +------+-------------+-------------+---------------+
## 
## Table: d3.2_m3rr2rc
## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |    nbar     |    4472     |     0.232     |
## +------+-------------+-------------+---------------+
## | Holm |    nbar     |    5700     |     0.184     |
## +------+-------------+-------------+---------------+
## 
## Table: d3.2_m3rr2rc